How to Solve equation using Eulers method in Matlab?

6 ビュー (過去 30 日間)
Samson David Puthenpeedika
Samson David Puthenpeedika 2021 年 11 月 14 日
コメント済み: Alan Stevens 2021 年 11 月 14 日
Question is as follows:-
Solve the following initial value problem over the interval from t = 0 to 1 where y(0) = 1.
dy/dt = yt^2 - 1.1y
• (a) analytically (showing the intermediate steps in the comments),
• (b) using the explicit Euler’s method with h = 0:5,
• (c) using the explicit Euler’s method with h = 0:25
Note: The Symbolic Math Toolbox should NOT be used.
Below is my code . I wanted to know my mistake if any.
%for h=0.5
h=0.5;
t=0:h:1;
y=zeros(size(t));
y(1)=1;
n=numel(y);
for i = 1:n-1
dydt= (y(i)*t(i).^2)-(1.1*y(i))
y(i+1) = y(i)+(dydt*h)
disp(y(i));
end
dydt = -1.1000
y = 1×3
1.0000 0.4500 0
1
dydt = -0.3825
y = 1×3
1.0000 0.4500 0.2587
0.4500
%for h=0.25
h1=0.25;
t1=0:h1:1;
y1=zeros(size(t1));
y1(1)=1;
n1=numel(y1)
n1 = 5
for i = 1:n1-1
dydt1= (y1(i)*t1(i).^2)-(1.1*y1(i))
y1(i+1)=y1(i)+(dydt1*h1)
disp(y1(i));
end
dydt1 = -1.1000
y1 = 1×5
1.0000 0.7250 0 0 0
1
dydt1 = -0.7522
y1 = 1×5
1.0000 0.7250 0.5370 0 0
0.7250
dydt1 = -0.4564
y1 = 1×5
1.0000 0.7250 0.5370 0.4229 0
0.5370
dydt1 = -0.2273
y1 = 1×5
1.0000 0.7250 0.5370 0.4229 0.3660
0.4229
Display in a plot
• the analytical result (a) as a black solid line, and
• the numerical results (b - c) as solid lines with point markers in different color
• with the corresponding labels of the axes and legend.
% analytical sol(plz check for this too)
T=[0 1]
T = 1×2
0 1
Y=[1 -0.766]
Y = 1×2
1.0000 -0.7660
% Graph
plot(t,y,'r',"DisplayName","h=0.5");
hold on
plot(t1,y1,'b',"DisplayName","h=0.25");
plot(T,Y,'k',"DisplayName","Anlaytical sol");
legend
grid on;

採用された回答

Alan Stevens
Alan Stevens 2021 年 11 月 14 日
Here's part (a) for you - definitely not a straight line!
  2 件のコメント
Samson David Puthenpeedika
Samson David Puthenpeedika 2021 年 11 月 14 日
Thankyou! is the rest part correct?
Alan Stevens
Alan Stevens 2021 年 11 月 14 日
Yes

サインインしてコメントする。

その他の回答 (0 件)

カテゴリ

Help Center および File ExchangeProgramming についてさらに検索

タグ

製品


リリース

R2021b

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by